Lie detectors are controversial instruments, barred from use as evidence in many

Question

Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no agreement, about the reliability of polygraph tests. Based on this research, suppose that a polygraph can detect 65% of lies, but incorrectly identifies 15% of true statements as lies. A certain company believes that 95% of its job applicants are trustworthy. What is the probability that a job applicant was actually trustworthy given they were rejected under suspicion of dishonesty?

Explanation / Answer

D: detected

L: Lie

P(D|L)=0.65

P(D|no L)=0.15

P(L)=1-0.95=0.05 and P(no L)=0.95

P(no L|D)=P(D|no L)*P(no L)/P(D)=P(D|no L)*P(no L)/(P(D|L)*P(L)+P(D|no L)*P(no L))

=0.15*0.95/(0.65*0.05+0.15*0.95)

=0.8143

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